Reprinted from16 June 1972, Volume 176, pp. 1191-1202 SCIENCE

The Decision to Seed Hurricanes

R. A. Howard, J. E. Matheson, D. W. North

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Copyright© 1972 by the American Association for the Advancement of Science

The Decision to Seed Hurricanes

On the basis of present information, the probability ofsevere damage is less if a hurricane is seeded.

R. A. Howard, J. E. Matheson, D. W. North

The possibility of mitigating the de-structive force of hurricanes by seedingthem with silver iodide was suggestedby R.H.. Simpson in 1961. Early exper-iments on hurricanes Esther (1961) andBeulah (1963) were encouraging (1), butstrong evidence for the effectiveness ofseeding was not obtained until the 1969experiments on Hurricane Debbie (2).Debbie was seeded with massive amountsof silver iodide on 18 and 20 August1969. Reductions of 31 and 15 percent inpeak wind speed were observed after theseedings.

Over the last 10 years property dam-age caused by hurricanes has averaged$440 million annually. Hurricane Betsy(1965) and Hurricane Camille (1969)each caused property damage of ap-proximately $1.5 billion. Any means ofreducing the destructive force of hur-ricanes would therefore have great eco-nomic implications.

Decision to Permit Operational Seeding

In the spring of 1970 Stanford Re-search Institute began a small study forthe Environmental Science ServiceAdministration (ESSA) (3) to exploreareas in which decision analysis (4, 5)might make significant contributions to

Dr. Matheson and Dr. North are with the decisionanalysis group, Stanford Research Institute, Menlo Park,California 94025. Dr. Howard is with the department ofengineering economic systems, Stanford University,Stanford, California 94305, and is a consultant to thedecision analysis group, Stanford Research Institute.

ESSA, both in its technical operationsand in its management and planningfunction. At the suggestion of MyronTribus, Assistant Secretary of Com-merce for Science and Technology, wedecided to focus the study on the de-cision problems inherent in hurricanemodification (6).

The objective of the present U.S. gov-ernment program in hurricane modifica-tion, Project Stormfury, is strictly scien-tific : to add to man's knowledge abouthurricanes. Any seeding of hurricanesthat threaten inhabited coastal areas isprohibited. According to the policy cur-rently in force, seeding will be carriedout only if there is less than a 10 per-cent chance of the hurricane centercoming within 50 miles of a populatedland area within 18 hours after seeding.

If the seeding of hurricanes threaten-ing inhabited coastal areas is to be un-dertaken, it will be necessary to modifythe existing policies. The purpose of ouranalysis is to examine the circumstancesthat bear on the decision to change ornot to change these existing policies.

The decision to seed a hurricanethreatening a coastal area should there-fore be viewed as a two-stage process: (i)a decision is taken to lift the presentprohibition against seeding threateninghurricanes and (ii) a decision is takento seed a particular hurricane a fewhours before that hurricane is expected tostrike the coast. Our study is con-centrated on the policy decision ratherthan on the tactical decision to seed aparticular hurricane at a particular

time. It is also addressed to the experi-mental question: What would be the valueof expanding research in hurricanemodification, and, specifically, what wouldbe the value of conducting additional fieldexperiments such as the seedings ofHurricane Debbie in 1969?

Our approach was to consider a rep-resentative severe hurricane bearing downon a coastal area and to analyze thedecision to seed or not to seed this "nominal" hurricane. The level of theanalysis was relatively coarse, because forthe policy decision we did not have toconsider many geographical andmeteorological details that might in-fluence the tactical decision to seed. Wedescribed the hurricane by a singlemeasure of intensity, its maximum sus-tained surface wind speed, since it isthis characteristic that seeding is ex-pected to influence (7). The surface winds,directly and indirectly (through the stormtide), are the primary cause of thedestruction wrought by most hurricanes(8). The direct consequence of a decision foror against seeding a hurricane is consideredto be the property damage caused bythat hurricane. (Injuries and loss of lifeare often dependent on the issuance andeffectiveness of storm warnings; theywere not explicitly included in ouranalysis.)

However, property damage alone isnot sufficient to describe the consequenceof the decision. There are indirect legaland social effects that arise from the factthat the hurricane is known to have beenseeded. For example, the governmentmight have some legal responsibility forthe damage caused by a seeded hurricane(9). Even if legal action against thegovernment were not possible, a strongpublic outcry might result if a seededhurricane caused an unusual amount ofdamage. Nearly all the governmenthurricane meteorologists that wequestioned said they would seed ahurricane threatening their homes andfamilies-if they could be freed fromprofessional liability.

The importance of the indirect effectsstems in large part from uncertaintyabout the consequences of taking eitherdecision. A hurricane is complex andhighly variable, and at present meteor-

ologists cannot predict accurately how thebehavior of a hurricane will evolve overtime. The effect of seeding is uncertainalso; consequently, the behavior of ahurricane that is seeded will be acombination of two uncertain effects:natural changes and the changes in-duced by seeding.

The seeding decision would remaindifficult even if the uncertainty wereremoved. Suppose that, if the hurricane isnot seeded, the surface wind intensifiesas shown by the curve w(t) in Fig. 1 andthat, if the hurricane is seeded, thebehavior of the wind is that shown by thecurve w'(t). The effect of the seeding hasbeen to diminish the wind, thus reducingproperty damage, yet the wind speed w'(t1)when the hurricane strikes land at time t1

ishigher than the wind speed when theseeding was initiated at time to. Even if thedecision maker were certain of w(t 1) andw'(t 1), he would still have a difficult choice.If he chooses not to seed, the citizensmay have more property damage. On theother hand, if he chooses to seed, thecitizens may not perceive themselves asbetter off because of his decision.Instead, they may perceive only that thestorm became worse after the seeding andthey may blame the decision-maker forhis choice. The trade off betweenaccepting the responsibility for seedingand accepting higher probabilities of severeproperty damage is the crucial issue inthe decision to seed hurricanes.

Decision under Uncertainty

The decision to seed a threateninghurricane would be taken about 12 hoursbefore the hurricane is predicted to strikethe coast. At this time the con-

sequences are uncertain for both alterna-tives; the decision-maker does not knowwhat amount of property damage will besustained if the hurricane is seeded or isnot seeded. We may illustrate thesituation facing him in the form of adecision tree, as shown in Fig. 2. Thedecision-maker must select one of the twoalternatives, seeding or not seeding. Thedecision cannot be avoided for inactionis equivalent to selecting the alternativeof not seeding. Each alternative leads to aset of possible consequences: propertydamage caused by the hurricane and theresponsibility incurred by thegovernment. These consequences are, inturn, related to the intensity of thehurricane and whether or not it wasseeded. The consequences for eachalternative are uncertain at the time thedecision is made; the uncertainty willbe resolved after the decision-makerselects his choice. This decision underuncertainty may be examined accordingto the usual procedures of a decisionanalysis. We use the information that iscurrently available to develop aprobability distribution over changes inthe intensity of the hurricane as measuredby its maximum sustained surface windspeed for each of the two decisionalternatives. Then we use data from pasthurricanes to infer a relation betweenwind speed and property damage. Byassessing the consequences in propertydamage and government responsibility andthe probability that these consequenceswill be achieved, we are able todetermine which of the decisionalternatives is the preferred choice.

Uncertainty in Hurricane Wind Changes

We began our analysis by consideringthe change in maximum sustained sur-face winds over a 12-hour period for ahurricane that is not seeded. If enoughdata had been available on the changes

in hurricane wind speeds with time, aprobability distribution for wind changescould have been based largely on thesepast data. Wind-change data were notavailable, but data were available forchanges over time in the central pres-sure of hurricanes. The central pressureand the maximum wind speed of a hur-ricane are closely related; Holliday hasshown that the available data can besummarized fairly well by a linear rela-tion (10). We combined this relation withobservations of the change in centralpressure over a 12-hour period, using theassumption that the discrepancies fromthe Holliday relation are independent overa 12-hour period and independent ofthe change in central pressure. Theseassumptions imply a probabilitydistribution on wind changes over a 12-hour period that is normal with a meanof zero and a standard deviation of 15.6percent (11).

Therefore, present information isconsistent with rather large natural changesin hurricane intensity over a 12-hourperiod. There is about one chance in sixthat a hurricane whose maximumsustained wind speed is 100 miles perhour will intensify over a 12hour periodto a maximum wind speed of over 115miles per hour; there is also about onechance in six that the winds wouldnaturally diminish to less than 85 milesper hour. In assessing these probabilitiesonly general historical and meteorologicalinformation has been used. In a specifichurricane situation additionalmeteorological information might indicatethat the hurricane would be more likelyto intensify or more likely to diminish.

Effect of Seeding

The next step is to develop a prob-ability distribution for the wind speed ifthe hurricane is seeded. The change inwind speed over 12 hours would then be acombination of the natural changeoccurring in the hurricane and thechange caused by seeding. With the lim-ited data available it is reasonable toassume that the two effects would beindependent of each other and act in anadditive fashion; for example, if thenatural change is an intensification suchthat the maximum sustained wind speedis increased from 100 to (100 + x)percent, and if the effect of seeding is todiminish the maximum sustained windspeed from 100 to (100 - y) percent, thenet observed change over 12

Fig. 1. Maximum sus-tained winds over time.

hours is from 100 to (100 + x - y ) percent. A probability distribution has al-ready been assigned for natural changes;we need to assign a probability distribu-tion for the change caused by seeding. Indeveloping this probability distribution itis necessary to distinguish between theeffect of seeding on one hurricane andthe average effect of seeding on manyhurricanes. The effect of seeding on aparticular hurricane might be quitedifferent from its average effect.

After discussion with meteorologistsassociated with Project Stormfury, weconcluded that the major uncertaintyabout the effect of seeding would beresolved if we knew which of the fol-lowing mutually exclusive and collec-tively exhaustive hypotheses described theeffect of seeding:

1) H1, the "beneficial" hypothesis. Theaverage effect of seeding is to reducethe maximum sustained wind speed.

2) H2, the "null" hypothesis. Seedinghas no effect on hurricanes. No changeis induced in maximum sustained windspeed.

3) H3, the "detrimental" hypothesis. Theaverage effect of seeding is to increasethe maximum sustained wind speed.

The scientific basis for the "bene-ficial" hypothesis, H1, had its origins in theoriginal Simpson theory (1). It has beenmodified and strengthened by ProjectStormfury studies involving a computermodel of hurricane dynamics (1,12). Thishypothesis, in fact, motivated theformation of the Project Stormfuryresearch program. A possible basis for the"null" hypothesis, H ,2

is that seeding doesnot release enough latent heat to affectthe dynamics of the hurricane. The"detrimental" hypothesis, H3, has beenadded to complete the set.Meteorologists do not have a basis inphysical theory for H3 that iscomparable to that for H l or H2.

Even if we know which of the hy-potheses is true, there remain uncertain-ties about the effects of seeding. We nowdescribe the approach we followed increating a model to formalize existingknowledge about these uncertainties.Then we shall return to the hypotheses.

Let us suppose we have access to aclairvoyant who can tell us which hy-pothesis, H1, H2, or H3, represents theactual effect of seeding on hurricanes.What probability would we assign to the12-hour change in the maximum sus-

tained winds of a seeded hurricane foreach of his three possible answers? If theclairvoyant says H2 is true, the assignmentprocess is simple. Seeding has no effect, andthe same probabilities are assigned to thewind speed w' if the hurricane is seededas to the wind speed w if the hurricane isnot seeded (13).

P(w' | H2) = P(w) = fN(100%, 15.6%)

(1)

If H1 is the clairvoyant's answer, theprocess is more difficult. The averageeffect is known to be a reduction instorm intensity, but the amount of thisaverage reduction is uncertain. TheSimpson theory and the computer studiesindicate that a reduction of 10 to 20percent in wind speed should be ex-pected, with 15 percent as the mostlikely value. This information was sum-marized by assigning to the change inwind speed a normal probability distri-bution with a mean of -15 percent and astandard deviation of 7 percent. Anaverage reduction greater than 15percent is considered as likely as anaverage reduction less than 15 percent,and the odds are about 2 to 1 that theaverage reduction will lie between 22 and8 percent rather than outside thisinterval.

The effect of seeding on an individualhurricane would be uncertain even if theaverage effect of seeding were known.Odds of about 2 to 1 were consideredappropriate that the effect of

seeding would not differ from the aver-age effect by more than about 7 per-cent; thus, a normal distribution cen-tered at the average value with a stan-dard deviation of 7 percent was judged anadequate summary of the informationavailable on fluctuations in seedingeffects. Combining the uncertainty aboutfluctuations with the uncertainty aboutthe average effect leads to a probabilitydistribution for the effect of seeding aspecific hurricane that is normal with amean equal to -15 percent and a stan-dard deviation of 10 percent (14).

Adding the natural change in thehurricane over a 12-hour period to thechange resulting from seeding gives thetotal 12-hour change occurring in aseeded hurricane if hypothesis H1 is true.The probability distribution assigned tow' is then normal with a mean of 85percent and a standard deviation of 18.6percent (1-5):

P(w' | H1) = fN(85%, 18.6%) (2)

The development of a probabilitydistribution for w', if it is consideredthat H3 is true, proceeds in a similarway. The average change effected byseeding is described by a normal prob-ability distribution with a mean of +10percent and a standard deviation of 7percent. The fluctuations expected whenan individual hurricane is seeded arenormally distributed around the averagewith a standard deviation of 7 percent.Combining these uncertainties

Fig. 2. The seeding de-cision: decision tree.

Consequences

Property damageGovernment responsibility

Property damageGovernment responsibility

Maximum sustained wind 12 hours after seeding decision (%)

Fig. 3 (upper left). Probability distributions on 12-hour wind changes for the seeded and unseeded hurricane.Fig. 4 (right). Property damage plotted against maximum sustained wind speed.Fig. 5 (lower left). Probability distributions on property damage for the seeded and unseeded hurricane.

Property damage ($ million)

w, Maximum sustained surface wind speed (mph)

with the uncertainty about the naturalchange in the hurricane over a 12-hourperiod, we obtain a probability distribu-tion for w' that is normal with a mean of110 percent and a standard deviation of18.6 percent

P(w' | H3) = fN (110%, 18.6%) (3)

We have now developed probabilitydistributions for the wind speed w' over a12-hour period following the initiationof seeding for each of the threehypotheses. To obtain the probabilitydistribution for w' that represents pres-ent information about the change in aseeded hurricane, we multiply each ofthe above distributions by the proba-bility that is presently assigned to each ofthe hypotheses being true and sum overthe three hypotheses:

Assigning Probabilities to

the Hypotheses

The last element in developing aprobability distribution for w' is to as-sign the probabilities P(H 1), P (H2), and

P(H3). These probabilities should

take into account both present meteor-ological information and meteorologicalinformation before the results of the1969 Debbie experiments. The modelswe have just constructed allow us toexamine the effect of experimental ob-servations, such as the Debbie results, inrevising the probabilities assigned to thethree hypotheses. If a wind speed w' = uhas been observed after a seeding ex-periment, the posterior probabilities P(H i | u )are related to the probabilities P(H i)assigned before the experiment by Bayes'equation (5, 16, 17):

The extension to several independentexperiments is straightforward. TheDebbie results are considered as twoindependent experiments in which re-ductions of 31 and 15 percent in windspeed were observed over a 12-hourperiod. The posterior probabilities as-signed to the hypotheses are computedby multiplying together the appropriate

values of two normal probability densityfunctions. The probability densityfunction for the Debbie results if hy-pothesis Hi is true, P(u1= 69 percent, u2 =85 percent | Hi), is

P(69%, 85% | H1) = 1.50 x 2.14 =3.21P(69%, 85% | H2) = 0.372 x 1.64 = 0.61P(69%, 85% | H3) = 0.195 X 0.886 = 0.173

(7)

These numbers can be used to computethe posterior probabilities appropriate afterthe Debbie results from any set ofprobabilities assigned to the hypothesesbefore the Debbie results were known. Forexample, suppose that before the Debbieexperiments the three hypotheses H1, H2,and H3 were considered to be equallylikely, that is, each had a probability of1/3. Then, after the Debbie results areincorporated through Bayes' equation, thecorresponding posterior probabilitiesassigned to the hypotheses are

P(H1 | Debbie) =

3.21 x 1/3

3.21 x 1/3 + 0.61 x 1/3 + 0.173 x 1/3

= .81

P(H2 | Debbie) = .15

P(H3 | Debbie) = .04 (8)

where the denominator is

However, meteorologists did not believethat H1, H2, and H3 were equally likelybefore the Debbie experiments. Theythought that seeding was unlikely tohave any effect but that, if seeding didhave an effect, it was more likely to bea reduction in wind speed than an in-crease, because a reduction was ex-pected from both the Simpson theoryand the computer model studies. Fur-ther, the four field experiments thatwere conducted before Debbie all ledto no change or to reductions in themaximum wind speeds (1).

We determined probability assignmentsfor the three hypotheses to reflect presentinformation by two conditions: (i) BeforeDebbie, meteorologists believed that H1

was more likely than H3 if seeding hadany effect on a hurricane. (ii) SinceDebbie, meteorologists believe that H1

and H2 are equally likely.These conditions led us to use the

probabilities

P(H1) =.49P(H2) =.49 (9)P(H3) =.02

in our analysis. These posterior prob-abilities correspond to the pre-Debbieprobabilities

P(H1) = .15P(H2) = .75 (10)P(H3) =.10

This set of probability assignments im-plies that prior to Debbie the odds were3 to 1 that seeding would have no ef-fect but that, if seeding did have aneffect, the odds were 3 to 2 for windreduction rather than wind intensifica-tion. Since the Debbie results, thechance of seeding causing an averageintensification of hurricanes is assessedat 1 in 50, and the "null" hypothesis,H2, of no effect and the "beneficial"hypothesis, H1, of an average reductionare judged equally likely.

The probability assignments (Eq. 9 )representing present information werereviewed with Project Stormfury offi-cials before being used in the analysis.However, the results of the analysis arenot particularly sensitive to the specificnumbers, as we discuss below.

Probability Distributions on

Wind Speed

We now can compute the probabilitydistributions on wind speed for theseeding and not-seeding alternatives (fromEqs. 1-4 and Eq. 9). These dis-

tributions are plotted in Fig. 3 ascomplementary cumulative distributionfunctions. By reading the ordinate val-ues corresponding to an initial windintensity of 100 percent, we find that theprobability assigned to intensification ifa hurricane is seeded is .36; if thehurricane is not seeded, the prob-ability is .50. The probability of inten-sification by 10 percent or more is .18 ifa hurricane is seeded and .26 if it isunseeded. For any particular windspeed, the probability that this speedwill be exceeded is always greater if thehurricane is unseeded than if it isseeded because the complementarycumulative distribution function for thenot-seeding alternative is always abovethe curve for the seeding alternative.This result is called stochastic domi-nance of the seeding alternative.

We have now specified the uncer-tainties about the outcome of the de-cision to seed. The same methods couldbe applied if the outcome were specifiedby several variables rather than simplyby the relative change in maximum sus-tained wind speed. Much of the uncer-tainty in the outcome is the result ofuncertainty about the natural change inhurricane behavior, not about the effectof seeding. This characteristic holdseven more strongly if other aspects ofhurricane behavior are examined, such asthe trajectory of a hurricane or theprecipitation it generates. Although it isconsidered unlikely that seeding wouldhave a significant effect on these featuresof hurricanes, substantial variations mayoccur from natural causes.

The uncertainty about the naturalbehavior of a hurricane makes the is-sue of government responsibility ofparamount importance. The intensifica-tion after seeding illustrated in Fig. 1 isa distinct possibility. Even if furtherexperiments confirm that the "bene-ficial" hypothesis H1, is true, there wouldstill be about one chance in ten that aseeded hurricane will intensify by 10percent or more. Meteorologicaladvances and improved computer modelsmay eventually allow many of thenatural changes in a hurricane to bepredicted accurately, but this capabilitymay require many years to achieve.

Wind Changes and Property Damage

The winds of a hurricane cause prop-erty damage directly and indirectly, thelatter by creating a high storm tide thatcan flood low-lying coastal areas.

The data available for past hurricanesdo not distinguish wind and storm-tidedamage; consequently, a detailed basis islacking for a causal model relatingwind and property damage. In ouranalysis, we assumed a general powerlaw of the form

d = c1wc2 (11)

where d is property damage in millions ofdollars, w is the maximum sustained windspeed in miles per hour, and c1 and c2

are empirical constants to be determinedfrom historical data on hurricanes. Weestimated c2 from data obtained from theAmerican Red Cross on residentialdamage from 21 hurricanes. Since theRed Cross data were available forcounties, we could isolate the damagecaused by precipitation-induced floodingrather than by the wind or the storm tideby assuming that such damage occurredwell inland. (The Red Cross data arethe only statistics available that permiteven this crude distinction betweencauses of damage.) Corrections forconstruction cost inflation and populationgrowth were included, and c2 wasdetermined as 4.36 by a linear least-squares fit of the logarithms (Fig. 4).Thus, a change in the wind speed by afactor x implies a change in propertydamage by the factor x to the power 4.36.If x is 0.85, corresponding to a 15 percentreduction in maximum wind speed, thecorresponding reduction in propertydamage is 51 percent (18).

The approximations of this method andthe limited data indicate that broad limitsare appropriate in a sensitivity analysis. Ifc2 is 3, the reduction in damagecorresponding to a 15 percent reductionin wind speed is 39 percent; if c2 is 6, thecorresponding damage reduction is 62percent.

Since the probability assignments towind changes were made on relativerather than absolute changes in maxi-mum sustained wind speeds, the scalingfactor c1 can be assigned as the last stepin the analysis. We assume a nominalhurricane whose maximum wind speedat the time of the seeding decision issuch that, if no change occurs in the12 hours before landfall, the propertydamage will be $100 million. Theanalysis for a more or a less severehurricane can be obtained by a suitablechange in scale factor (19).

Using this relationship between prop-erty damage and maximum wind speed,we can develop the probability distri-butions for property damage for thenominal hurricane, whether seeded orunseeded. Figure 5 shows that the seed-

ing alternative stochastically dominates thenot-seeding alternative : the probability ofexceeding a particular amount of propertydamage is always greater if the hurricaneis not seeded than if it is seeded. Hence,if property damage is the criterion, thebetter alternative is to seed.

Further Analysis of the

Decision to Seed

The decision to seed is shown in theform of a decision tree in Fig. 6. Thedecision to seed or not to seed is shownat the decision node denoted by thesmall square box; the consequent reso-

lution of the uncertainty about windchange is indicated at the chance nodesdenoted by open circles. For expositoryclarity and convenience, especially in thelater stages of the analysis, it isconvenient to use discrete approximationsto the probability distributions for windchange (20) (Table 1).

As a measure of the worth of eachalternative we can compute the expectedloss for each alternative by multiplyingthe property damage for each of the fivepossible outcomes by the probability thatthe outcome will be achieved andsumming over the possible consequences.The expected loss for the seedingalternative is $94.33 million (including acost of $0.25 million to

RESOLUTION OFUNCERTAINTY:

CHANGE IN PROPERTYMAXIMUM DAMAGE

SUSTAINED LOSSWIND (millions of

dollars)

carry out the seeding) ; the expected lossfor the not-seeding alternative is $116million; the difference is $21.67 millionor 18.7 percent.

These results should be examined tosee how much they depend on the spe-cific assumptions in the model. Sto-chastic dominance is a general result thatdoes not depend on the specific form ofthe relationship between propertydamage and maximum wind speed (seeEq. 11) ; rather, it depends on theprobabilities assigned to hypotheses H1, H2,and H3. The probability of H3 must beraised to .07 before stochastic dominanceno longer holds. Even if the probabilityof H3 is raised much higher, seeding stillresults in the least expected propertydamage. If P(H1) is .40, P(H2) is .40,and P(H3) is .20, the expected loss forthe seeding alternative is $107.8 million- 7 percent less than for the not-seedingalternative. Variation of the exponent c2

from 3 to 6 does not change the decision:if c2 is 3, the expected property damagewith seeding is 14 percent less; if c2 is 6,the expected reduction in damage is 22percent. If the criterion of expected costis replaced by a nonlinear utility functionreflecting aversion to risk, the relativeadvantage of the seeding alternative iseven greater (21). The results of extensivesensitivity analysis may be summarizedas follows : The expected loss in terms ofproperty damage appears to be about 20percent less if the hurricane is seeded.Varying the assumptions of the analysiscauses this reduction to vary between 10and 30 percent but does not change thepreferred alternative.

Government Responsibility

The analysis in the section aboveindicates that, if minimizing the expected loss in terms of property damage(and the cost of seeding) is the onlycriterion, then seeding is preferred.However, an important aspect of thedecision-the matter of governmentresponsibility-has not yet been in-cluded in the analysis. We have calcu-lated a probability of .36 that a seededhurricane will intensify between seedingand landfall and a probability of .18 thatthis intensification will be at least 10percent. This high probability is largelythe result of the great natural variabilityin hurricane intensity. It is advisable toconsider both the legal and the socialconsequences that might

+32% $335.8

+16 191.1

0 100.0

-16 46.7

-34 16.3

+32 335.8

+16 191.1

0 100.0

-16 46.7

-34 16.3

Fig. 6. The seeding decision for the nominal hurricane.

occur if a seeded hurricane intensified.

The crucial issue in the decision toseed a hurricane threatening a coastal areais the relative desirability of reducing theexpected property damage and assumingthe responsibility for a dangerous anderratic natural phenomenon. This isdifficult to assess, and to have a simpleway of regarding it we use the conceptof a government responsibility cost,defined as follows. The government isfaced with a choice between assuming theresponsibility for a hurricane andaccepting higher probabilities of propertydamage. This situation is comparable toone of haggling over price : Whatincrement of property-damage reductionjustifies the assumption of responsibilityentailed by seeding a hurricane? Thisincrement of property damage is definedas the government responsibility cost. Thegovernment responsibility cost is ameans of quantifying the indirect social,legal, and political factors related toseeding a hurricane. It is distinguishedfrom the direct measure-propertydamage-that is assumed to be the samefor both modified and natural hurricaneswith the same maximum sustained windspeed.

We define the government responsibilitycost so that it is incurred only if thehurricane is seeded. It is conceivable thatthe public may hold the governmentresponsible for not seeding a severehurricane, which implies that aresponsibility cost should also be at-tached to the alternative of not seeding.Such a cost would strengthen the impli-cation of the analysis in favor of per-mitting seeding.

The assessment of government re-sponsibility cost is made by consideringthe seeding decision in a hypotheticalsituation in which no uncertainty ispresent. Suppose the government mustchoose between two outcomes

1) A seeded hurricane that intensifies16 percent between the time of seedingand landfall.

2) An unseeded hurricane that inten-sifies more than 16 percent between thetime of seeding and landfall. The prop-erty damage from outcome 2 is x per-cent more than the property damagefrom outcome 1.

If x is near zero, the government willchoose outcome 2. If x is large, thegovernment will prefer outcome 1. Wethen adjust x until the choice becomesvery difficult; that is, the government isindifferent to which outcome it receives.For example, the indifference

Table 1. Probabilities assigned to wind changes occurring in the 12 hours before hurricanelandfall. Discrete approximation for five outcomes.

Interval of changes inmaximum sustained wind

Representativevalue in discrete

approximation

Probability that windchange will bewithin interval

( %) Ifseeded

If notseeded

Increase of 25% or more +32 .038 .054Increase of 10 to 25% +16 .143 .206Little change, +10 to -10% 0 .392 .480Reduction of 10 to 25% -16 .255 .206Reduction of 25% or more -34 .172 .054

point might occur when x is 30 percent.An increase of 16 percent in the inten-sity of the nominal hurricane corre-sponds to property damage of $191million, so that the corresponding re-sponsibility cost defined by the indifferencepoint at 30 percent is (.30) ($191 million),or $57.3 million. The responsibility costis then assessed for other possiblechanges in hurricane intensity.

The assessment of government re-sponsibility costs entails considerableintrospective effort on the part of thedecision-maker who represents the gov-ernment. The difficulty of determining thenumbers does not provide an excuse toavoid the issue. Any decision or pol-

icy prohibiting seeding implicitly deter-mines a set of government responsibilitycosts. As shown in the last section, seed-ing is the preferred decision unless thegovernment responsibility costs are high.

Let us consider an illustrative set ofresponsibility costs. The government isindifferent, if the choice is between:

1) A seeded hurricane that intensifies32 percent and an unseeded hurricanethat intensifies even more, causing 50percent more property damage.

2) A seeded hurricane that intensifies16 percent and an unseeded hurricanethat causes 30 percent more propertydamage.

CHANGE INMAXIMUM

SUSTAINEDW I N D

PROPERTY GOVERNMENT TOTALDAMAGE RESPONSIBILITY COST

(mil l ions ofCOST

(percent of (mil l ions

dollars) property damage) of dollars)$335.8 +50% $503.7

191.1 + 3 0 248.4

100.0 +5 105.0

46 .7 0 46 .7

16 .3 0 16 .3

335.8 - 335.8

191.1 - 101.1

100.0 -- 1 0 0

46 .7 - 46 .7

16 .3 - 16 .3

Fig. 7. The seeding decision for the nominal hurricane (government responsibility cost included).

3) A seeded hurricane that neitherintensifies nor diminishes (0 percentchange in the maximum sustained windspeed after the seeding) and an un-seeded hurricane that intensifies slightly,causing 5 percent more property dam-age.

4) A seeded hurricane that dimin-ishes by more than 10 percent and anunseeded hurricane that diminishes bythe same amount. (If the hurricanediminishes after seeding, everyone agreesthat the government acted wisely; thus,responsibility costs are set at zero.)

(1969) and Betsy (1965) were, an averageresponsibility cost of $200 million wouldbe needed. In other words, an expectedreduction of $200 million in propertydamage would be foregone if thegovernment decided not to accept theresponsibility of seeding the hurricane.

The importance of the responsibilityissue led us to investigate the legal basis forhurricane seeding in some detail. Theseinvestigations were carried out by GaryWidman, Hastings College of the Law,University of California. A firm legalbasis for operational seeding apparentlydoes not now exist. The doctrine ofsovereign immunity provides thegovernment only partial and unpredictableprotection against lawsuits, and substantialgrounds for bringing such lawsuits mightexist (22). A better legal basis forgovernment seeding activities is neededbefore hurricane seeding could beconsidered other than as anextraordinary emergency action. Specificcongressional legislation may be the bestmeans of investing a governmentagency with the authority to seedhurricanes threatening the coast of theUnited States.

Value of Information

One of the most important concepts indecision analysis is the value of in-formation: How much it would be worthto make the decision after rather thanbefore uncertainty is resolved? In the caseof hurricane modification, how muchshould be the government pay to learnwhich of the three hypotheses, H1, H2, orH3, is actually true (23) ? We imagine thatthe government has access to aclairvoyant who has this informationand is willing to sell it to thegovernment, if he is paid before hemakes the information available. It iseasiest to understand the calculation interms of the decision to seed one hurri-cane threatening a coastal area.

Let us consider the choice between thetwo decision situations shown in Fig. 8.The government can choose to buy theinformation and make the decision afterit has learned which hypothesis is true,or it can choose not to buy theinformation and can make the seedingdecision on the basis of the presentuncertainty.

Let us, for the moment, consider onlyproperty damage and the cost of seedingand disregard government responsibilitycosts. If Hl is true, the preferred decision isto seed because the expected

The analysis of the seeding decisionwith these government responsibility costsincluded is diagramed in Fig. 7. Evenwith these large responsibility costs, thepreferred decision is still to seed.

The responsibility costs needed tochange the decision are a substantialfraction of the property damage causedby the hurricane. For the $100-millionhurricane chosen as the example for thissection, the average responsibility costmust be about $22 million to change thedecision. If the hurricane were in the $1-billion class, as Camille

PROPERTYDAMAGE(millions of

dollars)+32% $335.8

+16 191.10 100.0

-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

+32% 335.8+16 191.1

0 100.0-16 46.7-34 16.3

Fig. 8. Expected value of the clairvoyant's information-which hypothesis describes theeffect of seeding? (There is no government responsibility cost.)

loss is $69.42 million compared with aloss of $116.00 million for the alternativeof not seeding. If H2 is true, then bychoosing not to seed, the government savesthe $0.25-million cost of seeding; the lossexpected from property damage is thesame for both alternatives $116.00 million.If H3 is true, seeding is a poor choice; theexpected loss from property damage is$167.61 million, $51.61 million morethan for the alternative of not seeding.At the present time, the government doesnot know what the clairvoyant will say,but probabilities have been assigned tohis answers

P(H1) = .49

P(H2) = .49 (12)P(H3) = .02

The expected loss corresponding to thedecision situation in Fig. 8 is then com-puted by multiplying the probability ofeach of the clairvoyant's answers by theexpected loss associated with that answerand summing over the three possibleanswers

(.49) ($69.42) + (.49) ($116.00) +

(.02) ($116.00) = $93.17 million (13)

Comparing this with the expected lossfor the best alternative (seed) without theclairvoyant's information, which was $94.33 million, we see that it is $1.16 millionless. This difference represents theexpected value of the clairvoyant'sinformation in allowing the government tomake a better decision. It is a relativelysmall number compared with theexpected losses because the informationis not expected to be of much value---theprobability assignments indicate thatseeding is already a good idea. Withoutthe clairvoyant's information thegovernment should seed; with theclairvoyant's information, withprobability .49, the government will savethe cost of seeding ($0.25 million), andwith the low probability .02 it will avertthe potentially disastrous intensificationexpected from H3, saving $167.61 million -$116 million = $51.61 million. By thisreasoning we got the same answer asbefore for the value of information

(.49) ($0.25) + (.02) ($51.61) =

$1.16 million (14)and we can see that the value is verysensitive to the small probability as-signed to H3.

Now suppose that the governmentresponsibility costs assumed previously areincluded. The expected value of perfectinformation is then much higher

because, if H2 is true, the governmentresponsibility costs can be saved by notseeding. If the decision without perfectinformation is to seed, the expectedsaving from engaging the clairvoyant is

(.49) ($0.25 + $23.28) +

(.02) ($51.61 + $53.57) =$13.63 million (15)

This figure represents 11.75 percent ofthe expected property damage if thealternative of not seeding is taken for thenominal 'hurricane.

The value of information largely de-rives from the fact that it allows thegovernment to avoid the responsibility forseeding if seeding turns out to have noeffect. The large increase over the valuecomputed in Eq. 13 is due to thecontribution of the government respon-sibility costs. Most of the increase of $12.47million, namely $11.41 million, comesfrom the first or H2 term.

The value of information depends onthe extent to which the government iswilling to assume responsibility for seedinga hurricane. If responsibility were not anissue, the government would seedoperationally now, and informationwould have a comparatively low value inthe context of this decision. The value ofinformation is great-

est when the government responsibilitycosts are large enough to make the de-cision essentially even between seedingand not seeding. Still higher responsi-bility costs cause the value of informationto decrease (24).

Value of Further Seeding Experiments

The analysis of the value of a seedingexperiment is similar to the deter-mination of the value of the clairvoyant'sinformation. The difference is that theresolution of uncertainty is only partial.The information obtained in theexperiment is used in Bayes' equation(Eq. 5) to revise the prior probabilityassignments to the hypotheses. Theoriginal decision is then reevaluated withthe posterior probabilities (Fig. 9). Theresult of the experiment is uncertainwhen the decision to experiment is made;consequently, the value of ex-perimentation must be computed as anexpectation over the possible posteriordecision situations. The situation can bediagramed in tree form as shown in Fig.9.

The analysis for two experimentalseedings is given in Table 2 (25). Thevalues assumed above for the govern-

CHOICE OF TOTALWHETHER TO OPERATIONAL COST

PERFORM RESULT OF SEEDING (millions ofEXPERIMENT EXPERIMENT DECISION OUTCOME dollars)

+32%+16

0

$503.7248.4105.0

-16-34

46.716.3

+32% 503.7+16 248.4

0 105.0-16 46.7-34 16.3

+32% 503.7+16 248.4

0 105.0-16 46.7-34 16.3

+32% 503.7+16 248.4

0 105.0-16 46.7-34 16.3

Fig. 9. Value of a seeding experiment (government responsibility cost included).

ment responsibility costs have been used.The expected value of the experiment inimproving one operational seedingdecision is $5.39 million, slightly lessthan twice the value of a singleexperimental seeding and more than tentimes the assumed experimental cost,$0.50 million. This value represents 4.7percent of the expected property dam-age if the alternative of not seeding istaken. In the discrete version used inthe analysis, one of five possible value(see Table 1) is taken as representative ofthe observed change in hurricane intensityover a 12-hour period following seeding:- 34, - 16, 0, + 16, and + 32 percent.The order in which the results areobtained is not significant, and a totalof 15 pairs of results could be obtainedwith two experiments (Table 2). Thesepairs might be placed in three groups:favorable, unfavorable, and mixedresults. The probability of obtaining apair of favorable results (- 34, - 34; - 34,- 16; - 34, 0; and - 16, - 16 percent) (26)in the two experimental seedings is .327;a pair of results in this group wouldprovide substantial confirmation ofhypothesisH1.

For example, a repetition of the pair

Table 2. Evaluation of a future experimentwith two (independent) experimental seedings.Government responsibility cost is included.

of results obtained with Debbie in 1969(- 34, - 16 percent in the discrete ap-proximation) would lead to posteriorprobabilities of .89 for H1, .11 for H2, andless than .005 for H3. A probability of

.075 is computed for a pair of stronglyunfavorable results (0, +32; +16, +16;+16, +32; +32, +32 percent); in this casethe probability assigned to H1 would berevised strongly downward. The remainingmixed pairs of results do not significantlyconfirm or deny H1, and these results havea total probability of .595. Within thisgroup a small probability (.055) is ac-corded to conflicting results in the twoexperiments (- 34, + 16; - 34, + 32;-16, + 16; - 16, + 32 percent).

Another Approach to Determining the Value

of Seeding Experiments

The preceding discussion indicates thatthe value of experiments is sensitive tothe government responsibility costs thatare assumed in the analysis. We maywish to determine the value ofexperiments in a different manner inwhich the issue of government re-sponsibility is treated implicitly.

Suppose that operational seeding will bepermitted only after another successfulresult is obtained in a pair ofexperiments of the Debbie type. Thisapproximation gives a lower bound tothe value of experiments because only asuccessful experimental result is re-garded as valuable. Even if wind re-ductions are not observed, knowledgegained about the effects of seeding mayhave implications for future successfuloperational seeding.

The probability of a favorable pair ofresults in two experimental seedings of ahurricane was computed as .327. Iffavorable experimental results areobtained and a subsequent hurricane isseeded operationally, the expected reduction in property-damage losses is $37.88million. Even if government responsibilitycosts are included, the reduction inexpected losses is $26.80 million. Sincethese reductions occur with a probabilityof .327, the expected value of theexperiment in improving one operationaldecision is $12.40 million if only theproperty damage is considered and$8.77 million if the decrease in propertydamage is partially offset by thegovernment responsibility costs. Thefigures $8.77 million and $12.40 millionrepresent 7.6 and 10.7 percent,respectively, of the $116-millionproperty damage expected from the not-seeding alternative in the seedingdecision for the nominal hurricane.

We see that the value of experimentsis considerably higher than the valuescomputed earlier. This difference resultsfrom the high responsibility costsimplicit in the decision not to seed onthe basis of present information. It maybe a reasonable assumption that a badoutcome for the first seeding of a hur-ricane threatening a coastal area wouldhave much less severe legal and socialconsequences if it were preceded by an-other successful experiment. Therefore,lowering the government responsibilitycosts may be appropriate after anothersuccessful field experiment.

Generalizing the Value of

Additional Information

The preceding discussions are directedspecifically toward updating ourinformation about which hypothesis, H 1,H2, or H3, describes the effect of seeding onthe maximum sustained wind speed of ahurricane. The analysis has been donefor a single seeding decision for amoderately intense hurricanethreatening a coastal area. Per-

Observedchange

inwind speed

Priorprob-ability

ofobser-vation

Posterior probabilityof hypotheses

Subsequent operationalseeding decisionexpected values(million dollars)

U1 U2

H1

H2 H3

Losswithseedingalter-native

Losswith thebetteralter-native

Posteriorvalue ofperfectinforma-tion

- 34 - 34 .0441 .97 .03 <.005 79.87 79.87 0.80

- 34 - 16 .1009 .89 .11 <.005 84.67 84.67 2.68- 34 0 .1140 .77 .22 <.005 92.11 92.11 5.64- 16 - 16 .0684 .69 .30 <.005 97.08 97.08 7.53

.3274

- 34 +16 .0324 .65 .34 .01 100.16 100.16 9.06- 34 +32 .0078 .60 .37 .03 105.27 105.27 12.10- 16 0 .1915 .49 .51 .01 110.25 110.25 12.78- 16 +16 .0651 .34 .64 .02 120.07 116.00 13.05

0 0 .1610 .28 .70 .02 123.37 116.00 10.81- 16 +32 .0167 .29 .65 .06 126.05 116.00 11.15

0 +1 6 .1229 .18 .79 .03 131.35 116.00 6.78

.5974

0 +32 .0332 .14 .77 .09 138.02 116.00 5.51+16 +16 .0251- .10 .83 .07 138.62 116.00 3.98+16 +32 .0145 .08 .75 .17 148.37 116.00 3.02+32 +3 2 .0024 .05 .59 .36 165.72 116.00 1.98

.0752

Value of seeding decision with prior information 110.92Expected value of seeding decision with seeding experiments 105.53

Value of experiment 5.39Cost of experiment 0.50

Net expected value of experiment 4.89

feet information applies not only to asingle hurricane but to all hurricanesthat might be seeded operationally. Thenumerical results for the single nominalhurricane are summarized in the ex-treme left column of Table 3 and areextended to multiple hurricanes in theremaining columns.

Even if only half the hurricanes could beseeded because of tactical considerationshaving to do with precipitation,hurricane trajectory, and so on, theexpected annual benefit from perfectinformation is $26 million. If we assumethat only half the hurricanes could beseeded, and discount the expectedbenefits of perfect information for allfuture hurricane seasons at a discountrate of 7 percent, we arrive at $370million. This figure represents the valueof a "perfect" experiment that woulddetermine whether Hl is true.

A single repetition of the 1969 Hur-ricane Debbie experiment has an ex-pected value of $5.39 million in thecontext of the nominal hurricane, orabout 4.7 percent of expected propertydamage. For the decision to seed a sin-gle hurricane in the billion-dollar range,the expected value of the experiment isten times as high, about $50 million. Forone hurricane season the value is 4.7percent of $220 million, or $10.2million (it is assumed again that vari-ous tactical considerations might pre-clude seeding in half of the cases). Forall future hurricane seasons, with adiscount rate of 7 percent, the value is$146 million compared with an experi-mental cost of about $500,000. Thebenefit to cost ratio is therefore about300 . Even if only a single hurricaneseason is considered, the expected ben-efits are 20 times greater than the cost ofthe experiment and ten times the presentannual budget for Project Stormfury.

Experimental Capability Decision

The occurrence of hurricanes is arandom phenomenon. Therefore, it isuncertain whether there will be an op-portunity for an experimental seedingbefore the arrival of a threatening stormthat might be operationally seeded.Opportunities for experimental seedinghave been scarce. In the last few yearsthere have been only six experimentalseedings, and these have been conductedon three hurricanes, Esther (1961), Beulah (1963), and Debbie (1969) (7). Experimentalseedings have been limited to a small region

of the Atlantic Ocean accessible to air-craft based in Puerto Rico, and fewhurricanes have passed through thisregion.

There are many other regions of theocean where hurricanes might be foundthat satisfy the present criterion for ex-perimental seeding - that is, the hurri-cane will be seeded only if the proba-bility is less than .10 that it will comewithin 50 miles of a populated landarea within 18 hours after seeding.However, a decision to expand thepresent experimental capability of ProjectStormfury would need to be made wellbefore the experiment itself. Whereas theseeding itself requires only that anaircraft be fitted with silver iodidepyrotechnic generators, the monitoring ofthe subsequent development of thehurricane requires other aircraft fittedwith the appropriate instrumentation. Therequirements in equipment, crewtraining, and communications andsupport facilities are substantial. In ad-dition, permission may be needed fromnations whose shores might be threat-ened by the seeded hurricane. The ex-perimental decision, then, involves aninvestment in the capability to performan experimental seeding. Whether anexperiment is performed depends on theuncertain occurrences of hurricanes in theexperimental areas.

The expected time before another ex-perimental opportunity for ProjectStormfury's present capability is aboutone full hurricane season. There was noopportunity during 1970. Preliminaryestimates of the cost of a capability toseed hurricanes in the Pacific are about $1 million (27). The incidence ofexperimentally seedable hurricanes in thePacific appears to be more than twicethat in the Atlantic (28). Therefore, itappears advisable to develop a

capability to conduct experimental hur-ricane seeding in the Pacific Oceansince the benefits expected from thiscapability outweigh the costs by a factorof at least 5 (29).

Conclusions from the Analysis

The decision to seed a hurricane im-poses a great responsibility on publicofficials. This decision cannot be avoidedbecause inaction is equivalent to adecision not to permit seeding. Eitherthe government must accept theresponsibility of a seeding that may beperceived by the public as deleterious, orit must accept the responsibility for notseeding and thereby exposing the publicto higher probabilities of severe stormdamage.

Our report to the National Oceanicand Atmospheric Administration rec-ommended that seeding be permitted onan emergency basis. We hope thatfurther experimental results and a for-mal analysis of the tactical decision toseed a particular hurricane will precedethe emergency. However, a decision maybe required before additional ex-perimental or analytical results areavailable. A hurricane with the intensityof Camille threatening a populouscoastal area of the United States wouldconfront public officials with an agoniz-ing but unavoidable choice.

The decision to seed hurricanes cannot be resolved on strictly scientificgrounds. It is a complex decision whoseuncertain consequences affect manypeople. Appropriate legal and politicalinstitutions should be designated formaking the hurricane-seeding decision, andfurther analysis should be conducted tosupport these institutions in carrying outtheir work.

Table 3. Summary of the value of additional information on the effect of seeding. Only the 50percent of hurricanes that are assumed to be possible candidates for seeding on the basis oftactical considerations are considered. If all hurricanes are assumed to be candidates foroperational seeding, the figures of the last two columns should be doubled.

Item

Nominal hurricaneused in analysis Single

hurricaneseason

(milliondollars)

All futurehurricaneseasons,

discountedat 7%

(milliondollars)

Milliondollars

Per-cent-age

Expected property damage without seeding 116.0 100.0 220.0 3142Expected value of perfect information 13.6 11.8 26.0 370Expected value of a field experiment

consisting of two experimental seedings 5.4 4.7 10.2 146Expected value of field experiments:

With government responsibility costs 8.8 7.6 16.6 238Government responsibility costs = 0 12.4 10.7 23.5 335

* If it is assumed that prior operational seeding is not permitted.

Role of Decision Analysis

The results of a decision analysis dependon the information available at the time itis performed. Decision analysis shouldnot be used to arrive at a staticrecommendation to be verified by furtherresearch, rather it should be used as adynamic tool for making necessarydecisions at any time. Various sensitivityanalyses included here indicate how newinformation might be expected toinfluence policy recommendations.However, the advent of a severe hurricanewill necessitate a decision on the basis ofthe information then available.

The analysis of hurricane modificationpoints up a difficulty that is common inpublic decision-making on complextechnological issues. When theconsequences of deploying new tech-nology are uncertain, who will make thechoice? While many individuals or groupsmay share responsibility, decisionanalysis conceptually separates the rolesof the executive decision-maker, theexpert, and the analyst. The analyst'srole is to structure a complex problemin a tractable manner so that theuncertain consequences of the alternativeactions may be assessed. Various expertsprovide the technical information fromwhich the analysis is fashioned. Thedecision-maker acts for society inproviding the basis for choosing amongthe alternatives. The analysis provides amechanism for integration andcommunication so that the technicaljudgments of the experts and the valuejudgments of the decision maker may beseen in relation to each other, examined,and debated. Decision analysis makes notonly the decision but the decisionprocess a matter of formal record. Forany complex decision that may affectthe lives of millions, a decision analysisshowing explicitly the uncertainties anddecision criteria can and. should becarried out.

References and Notes

1. R. H. Simpson and J. S. Malkus, Sci. Amer. 211,27 (Dec. 1964).

2. R. C. Gentry, Science 168, 473 (1970).3. Now incorporated in the National Oceanic

and Atmospheric Administration.4. R. A. Howard, Proceedings of the Fourth

International Conference on OperationalResearch (Wiley, New York, 1966).

5. -----, IEEE Trans. Syst. Sci. Cybern. 4(1968), p. 211.

6. A detailed discussion of the research is to be found inthe project's final report [D. W. Boyd, R. A.Howard, J. E. Matheson, D. W. North, DecisionAnalysis of Hurricane Modification (Project 8503,Stanford Research Institute, Menlo Park, Calif.,1971)]. This report is available through the Na-tional Technical Information Service, U.S.Department of Commerce, Washington, D.C.,accession number COM-71-00784.

7. The meteorological information leading to this

approximation is discussed in detail in the SRI projectfinal report (6), especially appendix B. Meteorologistsconnected with Project Stormfury believe it highlyimprobable that seeding will cause any substantialchange in the course of the hurricane, and otherimportant consequences of seeding are not foreseen atthis time. We wish to stress that our role in thedecision analysis of hurricane modification has beento provide the methodology for analyzing a complexdecision with uncertain consequences. The specificassumptions have been provided by the hurricanemeteorologists associated with Project Stormfuryand by other experts in relevant fields. Because ofspace limitations these assumptions cannot bediscussed in detail in this article; the interestedreader is advised to consult the project's final report orcommunicate directly with the authors. The type ofseeding is assumed to be the same as that used inthe Hurricane Debbie experiments: massivemultiple seeding of the clouds in the outer eyewall-region with silver iodide. During September 1971,Project Stormfury conducted seeding experiments of adifferent type on Hurricane Ginger (R. C. Gentry,internal communication, National Oceanic andAtmospheric Administration, October 1971). TheGinger experiment involved the seeding of clouds inthe rain bands well outside the eyewall region. This"rainsector" experiment was selected because Gingerhad a large and poorly formed eyewall and wasjudged not to be a good subject for eyewall-regionseeding. Although some changes in cloudstructure and wind field occurred at a time whenthey might have been caused by seeding, thesechanges were minor compared with the dramaticchanges that occurred in Hurricane Debbie afterseeding. Because of the difference in type ofseeding, the Ginger results do not imply a need forrevision of the analysis or data presented in thisarticle.

8. In some hurricanes, such as Diane (1955) and Camille(1969), precipitation-induced inland flooding hasalso been an important cause of property damage.Seeding might cause some increase inprecipitation. In considering the policy decision topermit seeding we ignored these precipitationeffects, but they might sometimes be important in thedecision to seed a specific hurricane.

9. Throughout the analysis it is assumed thatseeding would be authorized and carried out bysome agency of the federal government.

10. C. Holliday, Technical Memorandum WBTM SR-45(Environmental Science Service Administration,Washington, D.C., 1969).

11. The details of the derivation of this probabilitydistribution are given in appendix B of (6). Theindirect approach of using the Holliday relationcombined with pressure change observations wasfirst suggested by R. C. Sheets of the NationalHurricane Research Laboratory.

12. S. L. Rosenthal, Technical Memorandum ERLTM-NHRL 88 (Environmental Science ServiceAdministration, Washington, D.C., 1970). See alsoProject Stormfury Annual Report 1970 (NationalHurricane Research Laboratory, Miami, 1971).

13. A probability distribution on an uncertain quantity xwill be denoted P(x) whether x takes on discrete orcontinuous values. If x is discrete, P(x) will be theprobability mass function; if x is continuous, P(x)will be the probability density function. Aprobability distribution of the normal or Gaussianfamily specified by its mean m and standard devia-tion σ will be denoted fx (m, σ).

14. The average effect of seeding and the fluctuationfrom the average may be regarded as(independent) normal random variables whose sumrepresents the effect of seeding on a specifichurricane. According to well-known results inprobability theory, this sum will be normallydistributed with a mean equal to the sum of the twomeans and a standard deviation equal to thesquare root of the sum of the squares of the twostandard deviations.

15. The effect of seeding and the natural change in thestorm are described as independent normal randomvariables and the total change is their sum. Theindependence assumption is judged an appropriatesummary of present knowledge; sensitivity to thisassumption is examined in (6). Importantassumptions such as this one were reviewed withProject Stormfury meteorologists. A letter to usfrom R. C. Gentry (October 1970) stated, "whileseeding may "affect different hurricanes by differ

ent amounts, we are not yet prepared to predict thesedifferences." The assumption of independence doesnot deny that there may be a relationship betweenthe natural change occurring in a hurricane and theeffect of modification. When information about thisrelationship becomes available, it should beincorporated into the analysis and the independenceassumption should be withdrawn.

16. H. Raiffa, Decision Analysis: Introductory Lectureson Choices Under Uncertainty (Addiscn-Wesley,Reading, Mass., 1968); M. Tribus, RationalDescriptions, Decisions, and Designs (Pergamon,New York, 1969).

17. D. W. North, IEEE Trans. Syst. Sci. Cybern. 4 (1968), p. 200.

18. The details of the calculation of c2 are given in (6).Similar relationships between maximum sustainedwind speed and property damage have been stated byother investigators [R. L. Hendrick and D. G.Friedman, in Human Dimensions in WeatherModificat ion, W. R. Derrick Sewell, Ed. (Univ. ofChicago Press, Chicago, 1966), pp. 227246]. InNovember 1971, D. G. Friedman communicated to ussome results from analyzing insurance claim data.He finds an exponent of 6.7; this value wouldlead to much larger reductions in propertydamage than were assumed in our analysis. Otherinvestigators have suggested an equation of theform d = c1 (w - w0)2, where c, and w0 are empiricalconstants (R. C. Gentry, private communication).

19. This procedure is an approximation, whichdepends on the fact that seeding costs are smallcompared with costs of property damage.

20. It is shown in (6) that the results are notsensitive to the discrete approximation.

21. For example, if an exponential utility functionwith a risk aversion coefficient of y = 0.001 isused, the difference between the certain equivalents forthe two alternatives increases from $21.67 millionto $24.2 million. Because of stochasticdominance, any risk attitude will always leaveseeding as the preferred alternative. Furtherdiscussion on risk preference may be found in (5)and (17).

22. These issues are discussed in detail in ap-pendixes E and F of (6).

23. In answering this question we assume that thegovernment is willing to pay up to $1 to avoid$1 of property damage.

24. It is possible for the responsibility costs to be sohigh that a hurricane would not be seeded even if itwere certain that Hl is true. This amount ofresponsibility cost implies that the governmentwould prefer an unseeded hurricane to a seededhurricane that caused only half as much propertydamage.

25. For these calculations a system of computerprograms for evaluating large decision trees,developed by W. Rousseau of Stanford ResearchInstitute, was used.

26. These discrete outcomes correspond to a reduction of10 percent or more. The discrete approximationsimplifies the analysis by restricting the number ofpossible experimental results. Earlier we consideredthe revision of probabilities based on the results ofthe 1969 Hurricane Debbie experiments. There the

discrete approximation was not used, but itwould have given equivalent results.

27. R. C. Gentry, personal communication. In arrivingat this figure it was assumed that military aircraftbased in the Pacific could be used in the seeding.

28. Project Stormfury Annual Report 1968 (NationalHurricane Research Laboratory, Miami, 1969).

29. The details of this calculation are given in (6).30. This article summarizes research performed for the

National Oceanic and Atmospheric Administration,U.S. Department of Commerce, contract 0-35172; theproject leader is D. W. North. The authorsacknowledge the substantial contribution of Dr.Dean W. Boyd. The authors also wish toacknowledge Professor Gary Widman of HastingsCollege of the Law, University of California, SanFrancisco, for legal research supporting the projectand Dr. Cecil Gentry, Dr. Robert Simpson, Dr.Joanne Simpson, and many others who have beenassociated with Project Stormfury for theirassistance and cooperation. The findings andconclusions presented are the sole responsibility ofthe authors and do not necessarily reflect theviews of the U.S. government or any of theindividuals mentioned above.